Unbounded ABE via Bilinear Entropy Expansion, Revisited

We present simpler and improved constructions of unbounded attribute-based encryption (ABE) schemeswith constant-size public parameters under static assumptions in bilinear groups. Concretely, we obtain: – a simple and adaptively secure unbounded ABE scheme in composite-order groups, improving upon a previousconstruction of Lewko and Waters (Eurocrypt ’11) which only achieves selective security;– an improved adaptively secure unbounded ABE scheme based on the k-linear assumption in prime-ordergroups with shorter ciphertexts and secret keys than those of Okamoto and Takashima (Asiacrypt ’12);– the first adaptively secure unbounded ABE scheme for arithmetic branching programs under static assump-tions. At the core of all of these constructions is a “bilinear entropy expansion” lemma that allows us to generate anypolynomial amount of entropy starting from constant-size public parameters; the entropy can then be used totransform existing adaptively secure “bounded” ABE schemes into unbounded ones.